Highly Scalable Geodynamic Simulations with HyTeG

High-resolution geodynamic simulations of mantle convection are essential to quantitatively assess the complex physical processes driving the large-scale tectonic phenomena that shape Earth’s surface. Accurately capturing small-scale features such as unstable thermal boundary layers requires global resolution on the order of 1 km, which renders traditional sparse matrix methods impractical due to prohibitive memory demands and low arithmetic intensity. Matrix-free methods offer a scalable alternative, enabling the solution of large-scale linear systems efficiently. In this work, we leverage the matrix-free Finite Element framework HyTeG to conduct large-scale geodynamic simulations that incorporate realistic physical models. We validate the framework through a combination of convergence studies and geophysical benchmarks. These include verifying the convergence rates of Finite Element solutions against analytical solutions and through community benchmarks, including test cases with temperature-dependent and nonlinear rheologies. Our scalability studies demonstrate excellent performance, scaling up to problems with about $10^{11}$ unknowns in the Stokes system.

@article{id3077,
  author = {Ilangovan, Ponsuganth and Kohl, Nils and Mohr, Marcus},
  doi = {10.5194/egusphere-2025-2552},
  journal = {EGUsphere},
  language = {en},
  note = {preprint},
  pages = {1-25},
  title = {Highly Scalable Geodynamic Simulations with HyTeG},
  year = {2025},
}

%O Journal Article
%A Ilangovan, Ponsuganth
%A Kohl, Nils
%A Mohr, Marcus
%R 10.5194/egusphere-2025-2552
%J EGUsphere
%G en
%O preprint
%P 1-25
%T Highly Scalable Geodynamic Simulations with HyTeG
%D 2025